Show that if e1 e2 e3 are independent then e1 is

Question

Question: Show that if E₁, E₂, E₃ are independent, then E₁ is independent from E₂∪E₃. (Hint. By the Distributive Law, P(E₁ ∩ (E₂ ∪ E₃)) = P((E₁ ∩ E₂) ∪ (E₁ ∩ E₃)). Using the formula for the probability of the union of two events (part (1) of Proposition 2.4-2) and the independence of E₁, E₂, E₃, write this as P(E₁)P(E₂) + P(E₁)P(E₃) - P(E₁)P(E₂ ∩ E₃) and finish the proof.)